MaplePrimes Questions

The matrix data[gridji,4] in my code has float undefined. Please, how do I handle it?

In part of my program, I have a loop that the iterative calculations are performed there. During running the program when it comes to the loop the memory usage become full in a short period of time and I face the memory shortage. Since my program is so long and huge, I only can show the loop part of it here, you may look at where is the problem of high memory usage in loop and how to deal with it. Any comment will be appreciated.

I again note that, this segment can not be run independently since it is a part of big program. I put it just to see and mmake comment if any.

M := 3; Nm := 1

w0 := Matrix(M+Nm, 1)

wd0 := Matrix(M+Nm, 1)

taim := 1

F0 := convert([seq(Quadrature(Quadrature(simplify(add(add(W[i, j, 4, r]*LegendreP(i, 1)*LegendreP(j, 0), i = 0 .. II), j = 0 .. JJ)), `ζ__1` = -1 .. 1, method = romberg[3]), `η__1` = -1 .. 1, method = romberg[3]), r = 1 .. M), seq(0, n = 1 .. Nm)], Matrix)

T := 1/(2*Pi*`ω__km`[M][2])

dt := (1/10)*T

0.1123479896110e-4

(1)

for i to M do tau[i](t) := tau[i] end do

for i to Nm do p[i](t) := p[i] end do

`α__N` := .5; `β__N` := .25; a__0 := 1/(`β__N`*dt^2); a__1 := `α__N`/(`β__N`*dt); a__2 := 1/(`β__N`*dt); a__3 := 1/(2*`β__N`)-1; a__4 := `α__N`/`β__N`-1; a__5 := dt*(`α__N`/(2*`β__N`)-1); a__6 := dt*(1-`α__N`); a__7 := `α__N`*dt

q := Matrix(1 .. M+Nm, 1 .. floor(taim/dt)+1)

dq := Matrix(1 .. M+Nm, 1 .. floor(taim/dt)+1)

ddq := Matrix(1 .. M+Nm, 1 .. floor(taim/dt)+1)

q(1 .. M+Nm, 1) := w0

dq(1 .. M+Nm, 1) := wd0

for i to M do tau[i] := q(i, 1) end do

for i to Nm do p[i] := q(M+i, 1) end do

ddq(1 .. M+Nm, 1) := 1/ML.(diff((diff(sin(`ω__b`*t__0), t__0))*LinearAlgebra:-Transpose(F0), t__0)-CL.dq(1 .. M+Nm, 1 .. 1)-KL.q(1 .. M+Nm, 1 .. 1)-eqMNL)

t__0 := dt

V := LinearAlgebra:-Transpose(convert([seq(Tau[i], i = 1 .. M), seq(P[i], i = 1 .. Nm)], Matrix))

Qn__2 := LinearAlgebra:-Transpose(Matrix(1, M+Nm))

Qn__3 := LinearAlgebra:-Transpose(Matrix(1, M+Nm))

External force

 

`ω__b` := 25

``

F := diff((diff(sin(`ω__b`*t), t))*LinearAlgebra:-Transpose(convert(F0, Matrix)), t)

``

s := 1

k__d := 100000

with(Student[NumericalAnalysis]); dt

``

Loop

 

for t from t__0 by dt to taim do EQ := KL.V+a__0*ML.V+a__1*CL.V-ML.(a__0*q(1 .. M+Nm, s .. s)+a__2*dq(1 .. M+Nm, s .. s)+a__3*ddq(1 .. M+Nm, s .. s))-CL.(a__1*q(1 .. M+Nm, s .. s)+a__4*dq(1 .. M+Nm, s .. s)+a__5*ddq(1 .. M+Nm, s .. s))-F-Qn__2-Qn__3; G := Matrix(M+Nm, proc (i, j) options operator, arrow; (diff(EQ[i], V[j, 1]))[1] end proc); G1 := 1/G; if t = t__0 then X[1] := 1/(CL*a__1+ML*a__0+KL).(F+ML.(a__0*q(1 .. M+Nm, s .. s)+a__2*dq(1 .. M+Nm, s .. s)+a__3*ddq(1 .. M+Nm, s .. s))+CL.(a__1*q(1 .. M+Nm, s .. s)+a__4*dq(1 .. M+Nm, s .. s)+a__5*ddq(1 .. M+Nm, s .. s))) else X[1] := q(1 .. M+Nm, s .. s) end if; for k to 11 do X[k+1] := eval(V-G1.EQ, Equate(V, X[k])) end do; q(1 .. M+Nm, s+1 .. s+1) := X[k]; ddq(1 .. M+Nm, s+1 .. s+1) := a__0*(q(1 .. M+Nm, s+1 .. s+1)-q(1 .. M+Nm, s .. s))-a__2*dq(1 .. M+Nm, s .. s)-a__3*ddq(1 .. M+Nm, s .. s); dq(1 .. M+Nm, s+1 .. s+1) := dq(1 .. M+Nm, s .. s)+a__6*ddq(1 .. M+Nm, s .. s)+a__7*ddq(1 .. M+Nm, s+1 .. s+1); Wxy2 := add(add(add(h*W[i, j, 2, o]*LegendreP(i, `&zeta;__2`)*LegendreP(j, `&eta;__2`)*q[o, s+1], i = 0 .. II), j = 0 .. JJ), o = 1 .. M); Wxy3 := add(add(add(h*W[i, j, 3, o]*LegendreP(i, `&zeta;__2`)*LegendreP(j, `&eta;__2`)*q[o, s+1], i = 0 .. II), j = 0 .. JJ), o = 1 .. M); Plt := plots:-implicitplot(Wxy2-Wxy3, `&zeta;__2` = -1 .. 1, `&eta;__2` = -1 .. 1, color = red, thickness = 2, gridrefine = 3); j := 111111; Hvs2 := 1; for i while i <= j do Pnt[i] := op([1, i], Plt); if Wxy2-Wxy3 = 0 then j := 0 elif convert(Pnt[i], string)[1] = "C" then j := 0 else a__e[i] := (1/2)*abs(max(Column(Pnt[i], 1))-min(Column(Pnt[i], 1))); if a__e[i] = 0 then a__e[i] = 0.1e-5 end if; b__e[i] := (1/2)*abs(max(Column(Pnt[i], 2))-min(Column(Pnt[i], 2))); if b__e[i] = 0 then b__e[i] = 0.1e-5 end if; xc[i] := (max(Column(Pnt[i], 1))+min(Column(Pnt[i], 1)))*(1/2); yc[i] := (max(Column(Pnt[i], 2))+min(Column(Pnt[i], 2)))*(1/2); Hv2[i] := ((`&zeta;__2`-xc[i])/a__e[i])^2+((`&eta;__2`-yc[i])/b__e[i])^2-1; Hvs2 := Hv2[i]*Hvs2 end if end do; Qn__2 := LinearAlgebra:-Transpose(convert([(1/2)*k__d*Grid:-Seq(Quadrature(Quadrature(Heaviside(-Hvs2)*abs(Wxy2-Wxy3)*add(add(W[i, j, 2, r]*LegendreP(i, `&zeta;__2`)*LegendreP(j, `&eta;__2`), i = 0 .. II), j = 0 .. JJ), `&zeta;__2` = -1 .. 1, method = romberg[5]), `&eta;__2` = -1 .. 1, method = romberg[5]), r = 1 .. M), seq(0, n = 1 .. Nm)], Matrix)); Qn__3 := -Qn__2; s := s+1 end do

``

Download HighMemUseProb.mw

Hello everyone,

I want to use "proc" in a program. Although the original code is good for me, I modify it by "proc" to be convenient. Thank you very much!

With regards


clearall;
restart;
Digits := 15;
## Initial polygon
x[1] := [-1, 1/2, 1, 0, -sqrt(2)/2, -1, 1/2, 1, 0, -sqrt(2)/2, -1, 1/2, 1, 0, -sqrt(2)/2];
y[1] := [0, sqrt(3)/2, 0, -1, -sqrt(2)/2, 0, sqrt(3)/2, 0, -1, -sqrt(2)/2, 0, sqrt(3)/2, 0, -1, -sqrt(2)/2];
s2 := [-1, 1/2, 1, 0, -sqrt(2)/2, -1];
t2 := [0, sqrt(3)/2, 0, -1, -sqrt(2)/2, 0];
assign(a[-6] = 13/1296, a[-5] = -11/648, a[-4] = -1/16, a[-3] = -107/1296, a[-2] = 179/1296, a[-1] = 9/16, a[0] = 137/144, a[1] = 137/144, a[2] = 9/16, a[3] = 179/1296, a[4] = -107/1296, a[5] = -1/16, a[6] = -11/648, a[7] = 13/1296);

L := 3;
N := numelems(x[1]);
## Perform k-1 iterative steps
# L--the number of iterations; nk--the number of refined points after k steps;
for k to L do
    nk := 3^(k - 1)*(N - 6) + 6;
    for i from 3 to nk - 2 do
        x[k + 1][3*i - 8] := a[-6]*x[k][i + 2] + a[-3]*x[k][i + 1] + a[0]*x[k][i] + a[3]*x[k][i - 1] + a[6]*x[k][i - 2];
        y[k + 1][3*i - 8] := a[-6]*y[k][i + 2] + a[-3]*y[k][i + 1] + a[0]*y[k][i] + a[3]*y[k][i - 1] + a[6]*y[k][i - 2];
        x[k + 1][3*i - 7] := a[-5]*x[k][i + 2] + a[-2]*x[k][i + 1] + a[1]*x[k][i] + a[4]*x[k][i - 1] + a[7]*x[k][i - 2];
        y[k + 1][3*i - 7] := a[-5]*y[k][i + 2] + a[-2]*y[k][i + 1] + a[1]*y[k][i] + a[4]*y[k][i - 1] + a[7]*y[k][i - 2];
        x[k + 1][3*i - 6] := a[-4]*x[k][i + 2] + a[-1]*x[k][i + 1] + a[2]*x[k][i] + a[5]*x[k][i - 1];
        y[k + 1][3*i - 6] := a[-4]*y[k][i + 2] + a[-1]*y[k][i + 1] + a[2]*y[k][i] + a[5]*y[k][i - 1];
    end do;
end do;
## Plot the result
s1 := evalf(simplify(convert(x[L+1], list))):t1 := evalf(simplify(convert(y[L+1], list))):
f1 := <<s1> | <t1>>: f2 := <<s2> | <t2>>:
plot([f1, f2], linestyle = [1, 3], color = [black, red]);

T5Scheme:=proc(x[1],y[1],L)          
local i,k,nk,result,N,a[-1],a[7],a[6],a[5],a[4],a[3],a[2],a[1],a[0],a[-2],a[-3],a[-4],a[-5];          N:=numelems(x[1]):         
   for k from 1 to L do              
 nk := 3^(k - 1)*(N - 6) + 6;         
     for i from 3 to nk - 2 do            
      x[k + 1][3*i - 8] := a[-6]*x[k][i + 2] + a[-3]*x[k][i + 1] + a[0]*x[k][i] + a[3]*x[k][i - 1] + a[6]*x[k][i - 2];                       y[k + 1][3*i - 8] := a[-6]*y[k][i + 2] + a[-3]*y[k][i + 1] + a[0]*y[k][i] + a[3]*y[k][i - 1] + a[6]*y[k][i - 2];                  x[k + 1][3*i - 7] := a[-5]*x[k][i + 2] + a[-2]*x[k][i + 1] + a[1]*x[k][i] + a[4]*x[k][i - 1] + a[7]*x[k][i - 2];                  y[k + 1][3*i - 7] := a[-5]*y[k][i + 2] + a[-2]*y[k][i + 1] + a[1]*y[k][i] + a[4]*y[k][i - 1] + a[7]*y[k][i - 2];                   x[k + 1][3*i - 6] := a[-4]*x[k][i + 2] + a[-1]*x[k][i + 1] + a[2]*x[k][i] + a[5]*x[k][i - 1];               
    y[k + 1][3*i - 6] := a[-4]*y[k][i + 2] + a[-1]*y[k][i + 1] + a[2]*y[k][i] + a[5]*y[k][i - 1];                   result[1]:=x[L+1]:           result[2]:=y[L+1]            
  end do;          
     end do;  
     return result  
  end proc:

I would like to insert a hyperling to a geogebra document but the hyperlink box deosn't appear to allow general files. Can this be done?

It may seem like a stupid question, but why is the first answer not complete, but the second imput is the same as what the book states?

I know you dont need to be able to read Dutch to understand that A = amplitude (amplitude), Omega = Hoekfrequentie (Angular frequency), and Varphi= Fasehoek (phase angle). 

They state that fc(0)= A*e^i*varpi, but it clearly shows that the equation on the left of the equal sign gives a "2" and on the right it gives "2+ 2*i*sqrt3".

Why is this so? It does not make things more easy if you can make "mistakes" like that by just asking the answer, but maple spits out half an answer... 

He thanks a lot guys!

Greetings,

The Function 

p.s.
I scanned my math books, i like it, i can search in the book now with the "ctrl+f" function in Adobe reader. Get a scanner. Mine is a Canon Lide 400. Not regretting it.. :) 
Download Mapleprimes_Book_2_Question_3.6.mw
 

omega := 5

5

(1)

`&varphi;` := (1/3)*Pi

(1/3)*Pi

(2)

A := 4

4

(3)

"f(t):=A*cos(omega*t+`&varphi;`)""+A*I*sin(omega*t+`&varphi;`)"
 

proc (t) options operator, arrow, function_assign; A*cos(omega*t+varphi) end proc

 

(4*I)*sin((1/3)*Pi+5*t)

(4)

f(0)

2

(5)

A*exp(I*`&varphi;`)

2+(2*I)*3^(1/2)

(6)

NULL

``

Download Mapleprimes_Book_2_Question_3.6.mw

eq1 := f(r)*((diff(g(t, phi, r), t))*a^2+(diff(g(t, phi, r), t))*r^2+a*(diff(g(t, phi, r), phi)))/(sqrt(-g(t, phi, r)^2*f(r)^2+1)*sqrt(-(r^2+a^2*cos(theta)^2)*(2*M*r-a^2-r^2)))

f(r)*((diff(g(t, phi, r), t))*a^2+(diff(g(t, phi, r), t))*r^2+a*(diff(g(t, phi, r), phi)))/((-g(t, phi, r)^2*f(r)^2+1)^(1/2)*(-(r^2+a^2*cos(theta)^2)*(2*M*r-a^2-r^2))^(1/2))

(1)

eq2 := (((-a*cos(theta)^2+a)*f(r)^2*g(t, phi, r)^2+a*cos(theta)^2-a)*(diff(g(t, phi, r), phi, t))+(g(t, phi, r)^2*f(r)^2-1)*(diff(g(t, phi, r), phi, phi))+(-(diff(g(t, phi, r), phi))+(diff(g(t, phi, r), t))*a*(cos(theta)-1)*(cos(theta)+1))*(diff(g(t, phi, r), phi))*f(r)^2*g(t, phi, r))*f(r)/((-g(t, phi, r)^2*f(r)^2+1)^(3/2)*sin(theta))

(((-a*cos(theta)^2+a)*f(r)^2*g(t, phi, r)^2+a*cos(theta)^2-a)*(diff(diff(g(t, phi, r), phi), t))+(g(t, phi, r)^2*f(r)^2-1)*(diff(diff(g(t, phi, r), phi), phi))+(-(diff(g(t, phi, r), phi))+(diff(g(t, phi, r), t))*a*(cos(theta)-1)*(cos(theta)+1))*(diff(g(t, phi, r), phi))*f(r)^2*g(t, phi, r))*f(r)/((-g(t, phi, r)^2*f(r)^2+1)^(3/2)*sin(theta))

(2)

pdsolve([eq1, eq2])

Error, (in pdsolve/sys) found the element '_F4' repeated in the indication of blocks variables

 

``

Download problemfile.mw

I am trying to solve these two coupled PDE and am getting this error. Does anyone know what this mean?

What should I do to reduce evaluating time?

restart;

with(plots):

 

F:=kappa->kappa;

proc (kappa) options operator, arrow; kappa end proc

(1)

f:=(alpha,delta)->exp(-abs(F(kappa))^2*(1+delta^2)/2-abs(F(kappa))*alpha)/abs(F(kappa));

proc (alpha, delta) options operator, arrow; exp(-(1/2)*abs(F(kappa))^2*(1+delta^2)-abs(F(kappa))*alpha)/abs(F(kappa)) end proc

(2)

L:=(alpha,delta,Lambda)->(lambda^2*exp(-alpha^2/2)/4)*(Int(f(alpha,delta),kappa= -infinity..-Lambda)+Int(f(alpha,delta),kappa= Lambda..infinity));

proc (alpha, delta, Lambda) options operator, arrow; (1/4)*lambda^2*exp(-(1/2)*alpha^2)*(Int(f(alpha, delta), kappa = -infinity .. -Lambda)+Int(f(alpha, delta), kappa = Lambda .. infinity)) end proc

(3)

evalf(L(4,1,0.001));

0.8209373770e-3*lambda^2

(4)

g:=(beta,delta)->exp(-I*kappa*beta-abs(F(kappa))^2*(1+delta^2)/2)/abs(F(kappa));

proc (beta, delta) options operator, arrow; exp(-I*kappa*beta-(1/2)*abs(F(kappa))^2*(1+delta^2))/abs(F(kappa)) end proc

(5)

E:=(omega,gamma)->exp(I*omega*gamma)*(1-erf((gamma+I*omega)/sqrt(2)));

proc (omega, gamma) options operator, arrow; exp(I*omega*gamma)*(1-erf((gamma+I*omega)/sqrt(2))) end proc

(6)

J:=(alpha,delta,Lambda,beta,gamma)->(lambda^2*exp(-alpha^2/2)/8)*abs(Int(g(beta,delta)*(E(abs(F(kappa)),gamma)+E(abs(F(kappa)),-gamma)),kappa=-infinity..-Lambda)+Int(g(beta,delta)*(E(abs(F(kappa)),gamma)+E(abs(F(kappa)),-gamma)),kappa=Lambda..infinity));

proc (alpha, delta, Lambda, beta, gamma) options operator, arrow; (1/8)*lambda^2*exp(-(1/2)*alpha^2)*abs(Int(g(beta, delta)*(E(abs(F(kappa)), gamma)+E(abs(F(kappa)), -gamma)), kappa = -infinity .. -Lambda)+Int(g(beta, delta)*(E(abs(F(kappa)), gamma)+E(abs(F(kappa)), -gamma)), kappa = Lambda .. infinity)) end proc

(7)

#evalf(J(4,1,0.001,8,3));

N := (beta,alpha)-> (J(alpha,1,0.001,beta,3)-L(alpha,1,0.001))/\lambda^2;

proc (beta, alpha) options operator, arrow; (J(alpha, 1, 0.1e-2, beta, 3)-L(alpha, 1, 0.1e-2))/lambda^2 end proc

(8)

 

 

 

 

 

 

contourplot(evalf(N(beta,alpha)), beta=0..10,alpha=0..10,grid=[25,25]);

 

 

 

 

Download Negativity_v1.mw

Is there a problem with Maple primes?  

When I want to ask a question, the input panel is disabled and not possible to type into it. Here is screen shot.

 

Same when I wanted to make a reply to an answer. I can not type into the window that shows. It is like disabled.

I found I only can write here, in the post section.

What is the problem?  

Can we convert expression into determinant of 3 rows and 3 columns?

convert.mw

is their any comman to increase dpi such as 600,900 or prduced high quality graphs rather then increase or decraese in thickness of actual graph?

Good day everyone, 

Can I plot the graph of the sheet attached below such that x will be on the vertical component and y will be on the horizontal component? Can this be done on Maple? Anyone with useful information should please help.

plot_graph.mw

every time we past with windows button + v

it has the form of one liner math input i want to force all pasting to have normal math input !

example

i copy two items and past them (the last one with the windows button)

   a/b,  and x/y

and i get

x/y and a/b

or another example

i want to have a script that ones ran, makes all pasting that contains one liner into normal math

this is not a scrip we need to run at the end or periodically but a package ones loaded changes the way it pastes with the windows button (something like for every past "check IF it is a oneliner IF True, then make it into normal math, else stop)

or change a setting in maple via " := " that forces all math inputs to only be able to exist in normal math, ie. disable one liner math input.

the reason i know this is a setting problem and can be fixed (easily) is this

when we look at the clipboard folder both of them are actually formed by one liner math input. and only the older copyed item has the wrong form when pasting. just take a look at the clipboard folder

when i just use CTRL + V i get the first one (with the correct form), when i use windows button + v and select the second one (i get the second one but in the wrong form)

they dont look the samme (not the letters inside but the form)

so pls help this is a major problem in order to work effectively.

hello with the new online maple enviroment called "maple learn" can i use this to run maple on my ipad.

my main goal is to just open the files on the ipad when i am standing at a blackboard so i can tjeck and so i know what to write on the board.

are there other methods - if so i would like to hear them

i havent look at mapleNet could this be used.

PS: MAKING PDF IS NOT AN OPTIONS in general, and AS LONG AS THEY LOOK " so bad "

so just to not confuse i dont need to write formulas i just need to be able to look at my work in maple from an ipad.

and really important - i am noot looking to generate maplelearn files for everything. i want to find a normal maple file via the ipad via cloud/onedrive and open it. (no more) or login to maplelearn and open onedrive via file->open (and look through my files on the pc.

Every time I convert Mathematica expressions to Maple in order to use them there, I have to spend hrs by hand adding () around places in the input Mathematica expression because Maple complains about a^b^c.

The problem is that Mathematica has no problem with this, as it always takes a^b^c as a^(b^c). Here is an example to illustrate

But in Maple

MmaTranslator:-FromMma("E^x^2")

 

So I have to edit the input by hand

MmaTranslator:-FromMma("E^(x^2)")

The problem is that this is how Mathematica produces the expressions, and I have no way to tell Mathematica to put an extra () around to clear this ambiguity,

So I am hoping there is a way in Maple to do it. May be using some option? I know even using Maple own expressions, it complains about this:

x^y^z

But in Mathemtica it accepts this

If there is no way to change this behavior maple, else it means I have to spend hrs again editing all the Mathematica input by hand before using MmaTranslator:-FromMma each time. There are 100's of these in each file.

I think Maple here is not behaving the same as other CAS system. In Fricas it also works as is

(1) -> x^y^z

          z
         y
   (1)  x

Same in Maxima

(%i2) x^y^z;  
                                        z
                                       y
(%o2)                                x

Same in Giac

0>> x^y^z
x^(y^z)

And in every other CAS system I tried. It is only Maple who complain about this.

Any suggestions for workaround?

First 7 8 9 10 11 12 13 Last Page 9 of 2155